Answer:
The probability that no boats arrive is [tex]2.48\times 10^{-3}[/tex].
Step-by-step explanation:
Poisson distribution:
Poisson distribution is a statistical distribution that helps to find out the probability of a certain is likely occur a specified period of time.
[tex]P(X=x)=\frac{e^{-\lambda t}(\lambda t)^x}{x!}[/tex]
[tex]\lambda[/tex] = rate.
Given that, Poisson distribution at a rate of 3 per hour.
[tex]\lambda[/tex] = 3
t=2
x=0
The probability that no boats arrive is
[tex]P(X=0)=\frac{e^{-2\times 3}(2\times 3)^0}{0!}[/tex]
[tex]=2.48\times 10^{-3}[/tex]
The probability that no boats arrive will be [tex]2.48 \times 10^{-3}[/tex].
Given, boats arrive at the inlet drawbridge according to Poisson distribution at a rate of 3 per hour.
Now, we know that from poisson distribution, [tex]P (X=x) = \frac{e^{-Xt} (\lambda t)^x }{x!}[/tex]
Here, [tex]\lambda[/tex] [tex]=[/tex] rate
[tex]t = 2\\X = 0[/tex]
Now putting the above values in poissons equation we have,
[tex]P(X=0) = \frac{e^{-2\times3}(2\times3)^{0}}{0!} \\\\\\P = 2.48 \times 10^{-3}[/tex]
Hence the probability that no boats arrive will be [tex]2.48 \times 10^{-3}[/tex].
For more details on probability follow the link below:
https://brainly.com/question/795909
